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Piecewise Deterministic Processes in Biological Models

  • Ryszard Rudnicki
  • Marta Tyran-Kamińska

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Also part of the SpringerBriefs in Mathematical Methods book sub series (BRIEFSMATHMETH)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Ryszard Rudnicki, Marta Tyran-Kamińska
    Pages 1-32
  3. Ryszard Rudnicki, Marta Tyran-Kamińska
    Pages 33-62
  4. Ryszard Rudnicki, Marta Tyran-Kamińska
    Pages 63-82
  5. Ryszard Rudnicki, Marta Tyran-Kamińska
    Pages 83-114
  6. Ryszard Rudnicki, Marta Tyran-Kamińska
    Pages 115-128
  7. Ryszard Rudnicki, Marta Tyran-Kamińska
    Pages 129-147
  8. Back Matter
    Pages 149-169

About this book

Introduction

This book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models. Further, it presents examples of biological phenomena, such as gene activity and population growth, where different types of PDMPs appear: continuous time Markov chains, deterministic processes with jumps, processes with switching dynamics, and point processes. Subsequent chapters present the necessary tools from the theory of stochastic processes and semigroups of linear operators, as well as theoretical results concerning the long-time behaviour of stochastic semigroups induced by PDMPs and their applications to biological models.

 As such, the book offers a valuable resource for mathematicians and biologists alike. The first group will find new biological models that lead to interesting and often new mathematical questions, while the second can observe how to include seemingly disparate biological proc

esses into a unified mathematical theory, and to arrive at revealing biological conclusions.  The target audience primarily comprises of researchers in these two fields, but the book will also benefit graduate students.

Keywords

Deterministic Processes with Jumps Kolmogorov Equations Piecewise Deterministic Markov Processes Stochastic Differential Equations Stochastic Semigroups

Authors and affiliations

  • Ryszard Rudnicki
    • 1
  • Marta Tyran-Kamińska
    • 2
  1. 1.Institute of MathematicsPolish Academy of SciencesKatowicePoland
  2. 2.Institute of MathematicsUniversity of SilesiaKatowicePoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-61295-9
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-61293-5
  • Online ISBN 978-3-319-61295-9
  • Series Print ISSN 2191-530X
  • Series Online ISSN 2191-5318
  • Buy this book on publisher's site